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When the points in S are located in a simple polygon, we present an algorithm to compute G with multiplicative stretch [Formula: see text], and the number of edges in G (size of G) is [Formula: see text]. (2) When the points in S are located in the free space of a polygonal domain [Formula: see text] with h number of obstacles, we present an algorithm to compute G with multiplicative stretch [Formula: see text] and size [Formula: see text]. (3) When the points in S are located on a polyhedral terrain, we devise an algorithm to compute G with multiplicative stretch [Formula: see text] and size [Formula: see text].<\/jats:p>","DOI":"10.1142\/s1793830922500744","type":"journal-article","created":{"date-parts":[[2022,4,12]],"date-time":"2022-04-12T16:40:44Z","timestamp":1649781644000},"source":"Crossref","is-referenced-by-count":0,"title":["Vertex fault-tolerant spanners for weighted points in polygonal domains"],"prefix":"10.1142","volume":"15","author":[{"given":"R.","family":"Inkulu","sequence":"first","affiliation":[{"name":"Department of Computer Science and Engineering, IIT Guwahati, India"}]},{"given":"Apurv","family":"Singh","sequence":"additional","affiliation":[{"name":"Department of Computer Science and Engineering, IIT Guwahati, India"}]}],"member":"219","published-online":{"date-parts":[[2022,4,11]]},"reference":[{"key":"S1793830922500744BIB001","first-page":"186","volume-title":"Proc. Symp. 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